Name: ______Date: ______

Mr. Art Period: ______

Review # ______

Factoring

Part I: Mixed Review

Directions: Use your knowledge of factoring to answer the following questions below.

1. Expressed in factored form, the binomial 2x2y – 4xy3 is equivalent to:

(1) 2xy(x -2y) (3) 2xy(x – 2y2)

(2) 2xy(xy – 4y) (4) 2x2y3(y-2)

2. What is the GCF of 9xy – 54x2y3?

(1) 9 (3) 9xy

(2) xy (4) 6xy

3. One of the factors of x2 – 64 is:

(1) (x + 4) (3) 2x

(2) (x – 8) (4) (2x – 8)

4. A common factor of x2 + 7x +10 and x2 – 25 is:

(1) x -5 (3) x + 2

(2) x +5 (4) x2

5. One of the factors of 25x2 – 9 is 5x – 3. Find the other factor.

Part II: Greatest Common Factor (GCF)

Directions: Factor each of the following using the GCF Method

Review:

Step 1: Pull out the GCF and open parentheses

Step 2: Divide each term of the expression by the GCF and put in parentheses

6. 3x3 – 6x2 / 7. 24a2b + 18abc

Part III: Difference of Two Perfect Squares (DOTS)


Directions: Factor each of the following expressions using the DOTS Method.

Review:

Step 1: Open two sets of parentheses (one with a +, one with a - )

Step 2: Take the square root of each term and place them inside parentheses

8. x2 – 81 / 9. 4x2 – 25y2 / 10. 169 – k6

Part IV: Factoring Trinomials using the Product & Sum (P&S) Method

ax2 + bx + c

Review

Step 1: Find two numbers that add to “b” and multiply to “c”

Step 2: Place them in the parentheses in the blanks (x ___)

with + for positive numbers and – for negative numbers

Directions: Factor each of the following trinomials.

11. y2 + y - 20 / 12. 20 + 9x + x2

Part V: Factoring Completely

Review:

1. First look for a GCF. Factor using the GCF method, if possible.

2. Look inside the parentheses

·  Check for Difference of Two Perfect Squares (DOTS)

OR

·  Factor the trinomial

Directions: Factor each of the following expressions completely.

13. 3x2 + 15x + 12 / 14. 81x4 – 16y4

Part VI: Dividing a Polynomial by a Binomial

15. / 16. / 17.
18. (d2 + 4d – 32) ÷ (d - 4) / 19. / 20.

Part VII: Factoring Mixed Review

Directions: Factor each of the following expressions. Where necessary, factor the expressions completely.

21. 4y2 - 196 / 22. 2ax – 5x / 23. 5x2 - 45
24. 4x2 – 24x - 28 / 25. 49m2 – 100n2 / 26. x2 – x - 56
27. x4 - 1 / 28. 6x2 – 6y2 / 29. 2x3 – 8x
30. 5x2 + 20x + 20 / 31. 5x3 - 10x2 - 15x / 32. x2 + 3x - 4

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